In 3GPP LTE (3rd Generation Partnership Project Long-Term Evolution), RS's (Reference Signals) are used to estimate an uplink or downlink channel. Here, RS's include a DM (DeModulation)-RS used for channel estimation for data demodulation and an SRS (Sounding RS) used for channel quality estimation for frequency scheduling.
In an uplink of 3GPP LTE, a plurality of bandwidths are studied as an RS bandwidth. In Non-Patent Document 1, studies are underway to transmit a DM-RS by the same bandwidth as the data transmission bandwidth. Also, in Non-Patent Document 2, studies are underway to transmit an SRS by three bandwidths of 1.25 MHz, 5 MHz and 10 MHz. Here, the following explanation presumes that the transmission bandwidth and the number of RB's (Resource Blocks) are synonymous.
Also, in 3GPP LTE, studies are underway to use a ZC sequence, which is a kind of a CAZAC sequence, as an uplink RS. The time domain representation of a ZC sequence is represented by following equation 1.
      (          Equation      ⁢                          ⁢      1        )                                                          f              r                        ⁡                          (              k              )                                =                      {                                                                                                      exp                      ⁢                                              {                                                                                                                                            -                                j                                                            ⁢                                                                                                                          ⁢                              2                              ⁢                                                                                                                          ⁢                              π                              ⁢                                                                                                                          ⁢                              r                                                        N                                                    ⁢                                                      (                                                                                                                            k                                  ⁡                                                                      (                                                                          k                                      +                                      1                                                                        )                                                                                                  2                                                            +                              pk                                                        )                                                                          }                                                              ,                                                                                                              when                      ⁢                                                                                          ⁢                      N                      ⁢                                                                                                                        ⁢                                                                                                                      ⁢                      is                      ⁢                                                                                          ⁢                      odd                                        ,                                          k                      =                      0                                        ,                    1                    ,                    …                    ⁢                                                                                  ,                                          N                      -                      1                                                                                                                                                              exp                      (                                                                                                                                  -                              j                                                        ⁢                                                                                                                  ⁢                            2                            ⁢                                                                                                                  ⁢                            π                            ⁢                                                                                                                  ⁢                            r                                                    N                                                ⁢                                                  (                                                                                                                    k                                2                                                            2                                                        +                            pk                                                    )                                                                    }                                        ,                                                                                                              when                      ⁢                                                                                          ⁢                      N                      ⁢                                                                                                                        ⁢                                                                                                                      ⁢                      is                      ⁢                                                                                          ⁢                      even                                        ,                                          k                      =                      0                                        ,                    1                    ,                    …                    ⁢                                                                                  ,                                          N                      -                      1                                                                                                                                [          1          ]                    
Here, N is the sequence length, r is the ZC sequence number in the time domain, and N and r are coprime. Also, p is an arbitrary integer (generally p=0). Although a case will be explained below where the sequence length N is an odd number, a case is also possible where a sequence length N is an even number.
A cyclic shift ZC sequence acquired by cyclically shifting the ZC sequence represented by equation 1 in the time domain, or ZC-ZCZ (Zadoff-Chu Zero Correlation Zone) sequence is represented by following equation 2.
      (          Equation      ⁢                          ⁢      2        )                                                                                            f                                      r                    ,                    m                                                  ⁡                                  (                  k                  )                                            =                              exp                ⁢                                  {                                                                                                                                          -                            j                                                    ⁢                                                                                                          ⁢                          2                          ⁢                                                                                                          ⁢                          π                          ⁢                                                                                                          ⁢                          r                                                N                                            ⁢                                              (                                                                                                            (                                                              k                                ±                                                                  m                                  ⁢                                                                                                                                          ⁢                                  Δ                                                                                            )                                                        ⁢                                                          (                                                                                                k                                  ±                                                                      m                                    ⁢                                                                                                                                                  ⁢                                    Δ                                                                                                  +                                1                                                            )                                                                                2                                                )                                                              +                    pk                                    }                                                      ,                                                  ⁢                          when              ⁢                                                                                ⁢                                                                              ⁢              N              ⁢                                                          ⁢              is              ⁢                                                          ⁢              odd                        ,                          k              =              0                        ,            1            ,            …            ⁢                                                  ,                          N              -              1                                ⁢                                                                      [          2          ]                    
Here, m is the cyclic shift sequence number, and Δ is the cyclic shift value. The “±” sign may be either plus or minus. Also, the frequency domain sequence, transformed by performing Fourier transform of the time domain ZC sequence in equation 1, is also a ZC sequence. The frequency domain representation of a ZC sequence is represented by following equation 3.
      (          Equation      ⁢                          ⁢      3        )                                                                                            f                  u                                ⁡                                  (                  k                  )                                            =                              exp                ⁢                                  {                                                                                                              -                          j                                                ⁢                                                                                                  ⁢                        2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                        u                                            N                                        ⁢                                          (                                                                                                    k                            ⁡                                                          (                                                              k                                +                                1                                                            )                                                                                2                                                +                        qk                                            )                                                        }                                                      ,                                                  ⁢                          when              ⁢                                                          ⁢              N              ⁢                                                          ⁢              is              ⁢                                                          ⁢              odd                        ,                          k              =              0                        ,            1            ,            …            ⁢                                                  ,                          N              -              1                                ⁢                                                                      [          3          ]                    
Here, N is the sequence length, u is the ZC sequence number in the frequency domain, and N and u are coprime. Also, q is an arbitrary integer (generally q=0). Similarly, given that cyclic shift and phase rotation form a Fourier transform pair, a frequency domain representation of the time domain ZC-ZCZ sequence in equation 2 is shown in following equation 4.
      (          Equation      ⁢                          ⁢      4        )                                                                                            f                                      u                    ,                    m                                                  ⁡                                  (                  k                  )                                            =                              exp                ⁢                                  {                                                                                                                                          -                            j                                                    ⁢                                                                                                          ⁢                          2                          ⁢                                                                                                          ⁢                          π                          ⁢                                                                                                          ⁢                          u                                                N                                            ⁢                                              (                                                                                                            k                              ⁡                                                              (                                                                  k                                  +                                  1                                                                )                                                                                      2                                                    +                          qk                                                )                                                              ±                                                                                            j                          ⁢                                                                                                          ⁢                          2                          ⁢                                                                                                          ⁢                          π                          ⁢                                                                                                          ⁢                          Δ                          ⁢                                                                                                          ⁢                          m                                                N                                            ⁢                      k                                                        }                                                      ,                                                  ⁢                          when              ⁢                                                                                ⁢                                                                              ⁢              N              ⁢                                                          ⁢              is              ⁢                                                          ⁢              odd                        ,                          k              =              0                        ,            1            ,            …            ⁢                                                  ,                          N              -              1                                ⁢                                                                      [          4          ]                    
Here, N is the sequence length, u is the ZC sequence number in the frequency domain, and N and u are coprime. Also, m is the cyclic shift sequence number, Δ is the cyclic shift interval, and q is an arbitrary integer (generally, q=0).
With the ZC-ZCZ sequence represented by equation 4, two kinds of sequences of different sequence numbers (u) and sequences of different cyclic shift values (Δm), can be used for an RS (see FIG. 1). Here, sequences of different sequence numbers are semi-orthogonal (i.e. low-correlation and substantially orthogonal) to each other. On the other hand, sequences of different cyclic shift values are orthogonal to each other and therefore have good cross-correlation characteristics between sequences. Here, given the characteristics of CAZAC sequences, sequences of different cyclic shift values make it easy to provide orthogonality between cells between which frame synchronization is established.
Next, a specific method of generating an RS based on different transmission bandwidths (i.e. different numbers of RB's) will be described. Generally, (N−1) sequences can be generated from a ZC sequence of a prime-number sequence length N, so that it is possible to increase a sequence reuse factor compared to a case where the sequence length N is not a prime number. However, for example, in the system disclosed in Non-Patent Document 3, multiples of 12 subcarriers (corresponding to 1 RB) are determined as the number of subcarriers in the transmission band, and, if a ZC sequence of a prime-number sequence length is adopted, the ZC sequence length and the number of subcarriers in the transmission band do not match. To be more specific, when the transmission band is 2 RB's, although the number of subcarriers is 24, prime numbers close to 24 are 23 and 29, so that the ZC sequence length is 23 or 29.
Here, as a method of matching a ZC sequence of a prime-number sequence length N to the number of subcarriers in the transmission band, Patent Document 1 discloses cyclic extension and truncation. As shown in FIG. 2, cyclic extension refers to the method of using the maximum prime number as the sequence length, among the prime numbers less than the number of subcarriers in the transmission band, and, according to the number of subcarriers in the transmission band, copying the head part of the ZC sequence and attaching the head part to the tail end of that ZC sequence. On the other hand, truncation refers to the method of using the minimum prime number as the sequence length, among the prime numbers greater than the number of subcarriers in the transmission band, and, according to the number of subcarriers in the transmission band, removing part over the number of subcarriers from that ZC sequence.
Also, in Non-Patent Document 3, studies are underway to adopt, as the sequence length (N), the minimum prime number closest to the number of subcarriers, on a per transmission bandwidth (i.e. the number of RB's) basis. For example, when truncation is adopted, the sequence length is 13 in a bandwidth of 1 RB (i.e. 12 subcarriers), the sequence length is 29 in a bandwidth of 2 RB's (i.e. 24 subcarriers), and the sequence length is 37 in a bandwidth of 3 RB's (i.e. 36 subcarriers).    Patent Document 1: U.S. Patent Application Laid-Open No. 20050226140, specification    Non-Patent Document 1: TS36.211 V1.1.0, 3GPP TSG RAN, “Physical Channels and Modulation (Release 8)”    Non-Patent Document 2: NTT DoCoMo, Fujitsu, Mitsubishi Electric, NEC, Panasonic, Sharp, Toshiba Corporation, R1-072429, “Necessity of Multiple Bandwidths for Sounding Reference Signals”, 3GPP TSG RAN WG1 Meeting #49, Kobe, Japan, May 7-11, 2007    Non-Patent Document 3: Motorola, R1-071339, “Selection between Truncation and Cyclic Extension for UL RS Generation”, 3GPP TSG RAN WG1 Meeting #48bis, St. Julian's, Malta, Mar. 26-30, 2007